Well, [stat]->[10] gives the "creation" time, and the modification time is in 9; so you could do this:

my @sorted_files =
    map  { $_->[0] }
    sort { $a->[1] <=> $b->[1] or $a->[2] <=> $b->[2] }
    map  { [ $_, [stat]->[10], [stat]->[9] ] }
    @files;
[download]

But for some reason, I'm tempted to do this:

my @sorted_files =
    map  { $_->[0] }
    sort { $a->[11] <=> $b->[11] or $a->[10] <=> $b->[10] }
    map  { [ $_, stat ] }
    @files;
[download]